{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 构造人造数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def synthetic_data(w, b, num_examples):\n",
    "    \"\"\"generate y = Xw+b+noise.\"\"\"\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(X, w) + b\n",
    "    y += torch.normal(0, 0.01, y.shape )\n",
    "    return X, y.reshape((-1, 1))\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features: tensor([ 1.2272, -0.2920]) \n",
      "label: tensor([7.6485])\n"
     ]
    }
   ],
   "source": [
    "print('features:', features[0], '\\nlabel:', labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, 1].detach().numpy(),\n",
    "\t\t\t\tlabels.detach().numpy(), 1);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 读取小批量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 0.4600, -1.2205],\n",
      "        [ 1.7168, -0.4156],\n",
      "        [ 1.9387, -1.9374],\n",
      "        [-0.5701, -0.6344],\n",
      "        [ 1.4168,  0.8608],\n",
      "        [ 2.1690,  0.2075],\n",
      "        [ 0.9522,  0.9799],\n",
      "        [ 1.2027, -1.5078],\n",
      "        [-0.1661,  0.7356],\n",
      "        [-0.3900,  0.3088]]) \n",
      " tensor([[ 9.2713],\n",
      "        [ 9.0598],\n",
      "        [14.6648],\n",
      "        [ 5.2098],\n",
      "        [ 4.0878],\n",
      "        [ 7.8200],\n",
      "        [ 2.7649],\n",
      "        [11.7235],\n",
      "        [ 1.3640],\n",
      "        [ 2.3778]])\n"
     ]
    }
   ],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "\tnum_examples = len(features)\n",
    "\tindices = list(range(num_examples))\n",
    "\n",
    "\trandom.shuffle(indices)\n",
    "\tfor i in range(0, num_examples, batch_size):\n",
    "\t\tbatch_indices = torch.tensor(\n",
    "\t\t\tindices[i:min(i + batch_size, num_examples)])\n",
    "\t\tyield features[batch_indices], labels[batch_indices]\n",
    "\t\t\n",
    "batch_size = 10\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "\tprint(X, '\\n', y)\n",
    "\tbreak"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 定义初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b):\n",
    "\t\"\"\"线性回归模型\"\"\"\n",
    "\treturn torch.matmul(X, w) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):\n",
    "\t\"\"\"均方损失。\"\"\"\n",
    "\treturn (y_hat - y.reshape(y_hat.shape))**2 / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 定义优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):\n",
    "\t\"\"\"小批量随机梯度下降\"\"\"\n",
    "\twith torch.no_grad():\n",
    "\t\tfor param in params:\n",
    "\t\t\tparam -= lr * param.grad / batch_size\n",
    "\t\t\tparam.grad.zero_()\t# 下一次计算梯度不会跟上一次相关"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 训练过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.036826\n",
      "epoch 2, loss 0.000135\n",
      "epoch 3, loss 0.000049\n"
     ]
    }
   ],
   "source": [
    "# 指定超参数\n",
    "lr = 0.03\t\t# 学习率\n",
    "num_epochs = 3\t# 整个数据扫三遍\n",
    "net = linreg\t# 模型\n",
    "loss = squared_loss\t# 均方损失\n",
    "\n",
    "for epoch in range(num_epochs):\t# 每一次对数据扫一遍\n",
    "\tfor X, y in data_iter(batch_size, features, labels):\n",
    "\t\tl = loss(net(X, w, b), y)\t# 预测的y’和真实的y做对比，得到损失是一个长为batch_size的向量\n",
    "\t\tl.sum().backward()\t# 求和之后算梯度\n",
    "\t\tsgd([w, b], lr, batch_size)\t# 对w和b进行更新\n",
    "\t\n",
    "\t# 评价一下进度， 不需要计算梯度，所以放在no_grad里面\n",
    "\twith torch.no_grad():\n",
    "\t\ttrain_l = loss(net(features, w, b), labels)\n",
    "\t\t# print('epoch %d, loss %f' % (epoch + 1, train_l.mean().asnumpy()))\n",
    "\t\tprint(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 比较真实参数和通过训练学到的参数来评估训练的成功程度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差：tensor([ 7.6652e-05, -6.7067e-04], grad_fn=<SubBackward0>)\n",
      "b的估计误差：tensor([0.0003], grad_fn=<RsubBackward1>)\n"
     ]
    }
   ],
   "source": [
    "print(f'w的估计误差：{true_w - w.reshape(true_w.shape)}')\n",
    "print(f'b的估计误差：{true_b - b}')"
   ]
  }
 ],
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